Methods of calculating the deflection of an orthotropic inhomogeneous plate on an elastic basis

Lavrenyuk, M. V. (2019). Methods of calculating the deflection of an orthotropic inhomogeneous plate on an elastic basis. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(1), 106–109. https://doi.org/10.17721/1812-5409.2019/1.24

The problem of elastic equilibrium of an orthotropic nonhomogeneous rectangular plate on an elastic basis (one-parameter Winkler model) is considered, hingedly fixed from all sides. We use the Navier method for finding the deflection function at each step of the iterative process and perturbation methods and successive approximations as iterative methods for solving the problem. The suitability of the method of successive approximations and the method of perturbations for the numerical solution of the problem of determining the stress-strain state of such a plate, the limits of the applicability of these methods, their accuracy and convergence of the iterative process in solving the deformation problems of heterogeneous orthotropic plates have been analyzed.The dependence of the deflection on the mechanical and geometric parameters of the plate and the base is established. It was found that the Poisson ratio practically does not affect the stress state of the plate (when the Poisson ratio is changed two times, the difference between the intensities of the shear stresses does not exceed 10%), it is possible to consider it as a constant using the methods of successive approximations and disturbances. It is also established that the method of successive approximations and the method of perturbations has a limit on the nature of inhomogeneity, the convergence essentially depends on the nature of the heterogeneity.Key words: method of successive approximations, perturbation method, orthotropic inhomogeneous plate.Pages of the article in the issue: 106-109Language of the article: Ukrainian